### Abstract

irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibrium

within these biochemical reaction systems

Original language | English |
---|---|

Pages (from-to) | 675-688 |

Number of pages | 14 |

Journal | Journal of Mathematical Chemistry |

Volume | 52 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2014 |

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### Keywords

- complexity
- metabolic networks
- returnability
- centrality
- statistical mechanics
- environmental variability

### Cite this

*Journal of Mathematical Chemistry*,

*52*(2), 675-688. https://doi.org/10.1007/s10910-013-0288-7

}

*Journal of Mathematical Chemistry*, vol. 52, no. 2, pp. 675-688. https://doi.org/10.1007/s10910-013-0288-7

**A statistical mechanics description of environmental variability in metabolic networks.** / Crofts, J.J.; Estrada, Ernesto.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A statistical mechanics description of environmental variability in metabolic networks

AU - Crofts, J.J.

AU - Estrada, Ernesto

PY - 2014/2

Y1 - 2014/2

N2 - Many of the chemical reactions that take place within a living cell areirreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibriumwithin these biochemical reaction systems

AB - Many of the chemical reactions that take place within a living cell areirreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium with a hypothetical reference system, enables us to quantify the extent to which a metabolic network is in disequilibrium. Further, by introducing a new directed centrality measure via an extension of the subgraph centrality metric to directed networks, we are able to characterise individual metabolites by their participation within metabolic pathways. To demonstrate these ideas, we study 116 metabolic networks of bacteria. In particular, we find that the equilibrium constant for the metabolic networks decreases significantly in-line with variability in bacterial habitats, supporting the view that environmental variability promotes disequilibriumwithin these biochemical reaction systems

KW - complexity

KW - metabolic networks

KW - returnability

KW - centrality

KW - statistical mechanics

KW - environmental variability

U2 - 10.1007/s10910-013-0288-7

DO - 10.1007/s10910-013-0288-7

M3 - Article

VL - 52

SP - 675

EP - 688

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 2

ER -